I've heard that they should be left in until they are completely dry at the very least, before being moved to the brooder.
But then I've also heard, as PaganBird says, waiting until the hatch is complete.
I'll be setting my first time in about a week. So far, I'm of the mind of waiting until there are several hatched out and fluffy before moving them to the brooder. My reasoning for this is that my incubator (LG 5200 Still Air, modified with a fan) is a bit on the small side.
A neighbor friend is donating eggs from her flock for my first attempt and that could be as many as 20 or 30 eggs. In order to minimize the amount of rough treatment of the eggs yet to hatch by those who have hatched and are bouncing off of the walls, I'm thinking it's best to get them out of there as soon as possible!
Having said that, I can see the wisdom of keeping ones hands out of the bator until all the chicks who are going to hatch have hatched.
For me, I think the more important question is going to be: How will I know when the hatch is complete? I've heard by some accounts that it can take as much as 48-72 hours!
I'd hate to think it was all done, start moving chicks to the brooder only to find one or two more that were slow to pip, and all of a sudden they start! I'd feel real bad if I lost a couple of late bloomers because I had the incubator open too long.
Tough call CajunChick. I think you just have to go with what your gut tells you. Good luck with your entire hatch!